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A mixed multiscale spectral generalized finite element method

We present a multiscale mixed finite element method for solving second order elliptic equations with general L infinity\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \se...

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Hauptverfasser: Alber, Christian (VerfasserIn) , Ma, Chupeng (VerfasserIn) , Scheichl, Robert (VerfasserIn)
Dokumenttyp: Article (Journal)
Sprache:Englisch
Veröffentlicht: February 2025
In: Numerische Mathematik
Year: 2025, Jahrgang: 157, Heft: 1, Pages: 1-40
ISSN:0945-3245
DOI:10.1007/s00211-024-01446-3
Online-Zugang:Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1007/s00211-024-01446-3
Verlag, lizenzpflichtig, Volltext: https://link.springer.com/article/10.1007/s00211-024-01446-3#citeas
Volltext
Verfasserangaben:Christian Alber, Chupeng Ma, Robert Scheichl
Beschreibung
Zusammenfassung:We present a multiscale mixed finite element method for solving second order elliptic equations with general L infinity\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L<^>{\infty }$$\end{document}-coefficients arising from flow in highly heterogeneous porous media. Our approach is based on a multiscale spectral generalized finite element method (MS-GFEM) and exploits the superior local mass conservation properties of mixed finite elements. Following the MS-GFEM framework, optimal local approximation spaces are built for the velocity field by solving local eigenvalue problems over generalized harmonic spaces. The resulting global velocity space is then enriched suitably to ensure inf-sup stability. We develop the mixed MS-GFEM for both continuous and discrete formulations, with Raviart-Thomas based mixed finite elements underlying the discrete method. Exponential convergence with respect to local degrees of freedom is proven at both the continuous and discrete levels. Numerical results are presented to support the theory and to validate the proposed method.
Beschreibung:Gesehen am 12.03.2025
Online veröffentlicht: 13. Januar 2025
Beschreibung:Online Resource
ISSN:0945-3245
DOI:10.1007/s00211-024-01446-3

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